Journal of Applied Mathematics / 2012 / Article / Tab 4

Research Article

Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Table 4

Comparison of the macro-model to the micro-model for different values of πœ€ Example 3.5.

# cells πœ€ β€– 𝑒 𝑁 πœ€ β€– βˆ— , 𝐿 1 𝛼 1 β€– 𝑒 𝑁 πœ€ β€– βˆ— , 𝐿 2 𝛼 2

3 Γ— 3 1 / 3 1 . 1 8 2 6 Γ— 1 0 βˆ’ 2 β€” 3 . 2 0 4 8 Γ— 1 0 βˆ’ 2 β€”
5 Γ— 5 1 / 5 7 . 0 8 7 7 Γ— 1 0 βˆ’ 3 0 . 9 9 7 8 1 . 9 0 2 9 Γ— 1 0 βˆ’ 2 0 . 9 8 0 0
7 Γ— 7 1 / 7 5 . 0 4 9 7 Γ— 1 0 βˆ’ 3 0 . 9 9 2 4 1 . 3 5 1 8 Γ— 1 0 βˆ’ 2 0 . 9 8 4 0
9 Γ— 9 1 / 9 3 . 9 2 8 1 Γ— 1 0 βˆ’ 3 1 . 0 0 0 6 1 . 0 5 0 2 Γ— 1 0 βˆ’ 2 0 . 9 9 5 5